advanced methods for sequence analysis · sim4 [florea et al., 1998], spidey [wheelan et al., 2001]...

Advanced Methodsfor Sequence Analysis

Gunnar Rätsch

Friedrich Miescher Laboratory, Tübingen

Vorlesung WS 2007/2008Eberhard-Karls-Universität Tübingen

6 February, 2008

http://www.fml.mpg.de/raetsch/lectures/amsa07

Today

Cheng Soon Ong, Petra Philips and Gunnar Rätsch: Kernel Methods for Predictive Sequence Analysis: Introduction,

Three applicationsLearning parameters for spliced alignmentsDiscriminative Gene findingAnalysis of Resequencing Data

Summary of previous lectures

Max-Margin Structured Output Learning


Learn function f (y|x) scoring segmentations y for x

Maximize f (y|x) w.r.t. y for prediction:

argmaxy!Y"

f (y|x)

Given N sequence pairs (x1,y1), . . . , (xN,yN) for trainingDetermine f such that there is a large margin betweentrue and wrong segmentations

minf

CN!

n=1

!n + P[f ]

w.r.t. f (yn|xn) # f (y|xn) $ 1 # !n

for all yn %= y ! Y", n = 1, . . . , N

Exponentially many constraints!

Joint Feature Map


Recall the kernel trickFor each kernel, there exists a corresponding fea-ture mapping !(x) on the inputs such that k(x,x&) ='!(x), !(x&)(.

Joint kernel on X and YWe define a joint feature map on X ) Y, denoted by!(x, y). Then the corresponding kernel function is

k((x, y), (x&, y&)) := '!(x, y), !(x&, y&)(.

For multiclassFor normal multiclass classification, the joint feature mapdecomposes and the kernels on Y is the identity, that is

k((x, y), (x&, y&)) := [[y = y&]]k(x,x&).

Algorithm


1. Y1n = *, for n = 1, . . . , N

2. Solve(wt, !t) = argmin

w!F,!C

N!

n=1

!n + +w+2

w.r.t. 'w, !(x,yn) # !(x,y)( $ 1 # !n

for all yn %= y ! Ytn, n = 1, . . . , N

3. Find violated constraints (n = 1, . . . , N )

ytn = argmax

yn %=y!Y"'wt, !(x,y)(

If 'wt, !(x,yn) # !(x,ytn)( < 1 # !t

n, set Yt+1n = Yt

n , {ytn}

4. If violated constraint exists then go to 25. Otherwise terminate - Optimal solution


PALMA: Perfect Alignments using Large Margins

Gunnar Rätsch,1 Bettina Hepp,2 Uta Schulze,1,3 and ChengSoon Ong1,4

1 Friedrich Miescher Laboratory, Tübingen2 Fraunhofer FIRST, Berlin,

3 University of Leipzig4 Max Planck Institute for Biological Cybernetics, Tübingen

http://www.fml.mpg.de/raetsch/projects/palma

Motivation & Background


Abundant experimental data:Expressed Sequence Tags (EST)Full length mRNAs

Alignment to genomic sequences helpsDiscovery of new genes,Delineation exon/intron boundaries,Identification alternative splice forms,Finding SNPs, . . .

ProblemsRepetitive elements, paralogs, pseudo-genesSequencing errors, polymorphismsNon-canonical splice sitesMicroexons

Previous Work


More than 10 years of research on spliced alignmentsGreedy algorithms (extend seed words or Blast based)

Sim4 [Florea et al., 1998], Spidey [Wheelan et al., 2001]

Blat (prefers AG/GT) [Kent, 2002]

EST Genome (DP based, prefers AG/GS) [Mott, 1997]

Exalin (DP based, AG/GS only) [Zhang and Gish, 2006]

Fixed substitution and gap costsSplice site model (PWMs)

"Maximum likelihoodcombination

Why another tool?More accurate splice site models (SVM based)Intron length modelMore principled combination (based on large margins)

2-Class Splice Site Detection


True sites: fixed window around a true splice siteDecoys sites: generated by shifting the window

- Very unbalanced problem (1:200)- Millions of points from EST databases- Large scale methods necessary

(here: Support Vector Machines)

2-Class Splice Site Detection


Results on C. elegans 1-ROC Score[Rätsch and Sonnenburg, 2004] Donor AcceptorHigher order PWM 1.77% 1.12%SVM w/ TOP Kernel 1.68% 1.30%SVM w/ Polynomial 1.59% 1.05%SVM w/ Locality Improved 1.52% 0.92%SVM w/ Weighted Degree ’04 1.53% 0.95%SVM w/ Weighted Degree ’05 0.38% 0.26%

Weighted Degree kernel is simple and accurate:

Computes similaritybetween sequences

Allows training on 10 million examples [Sonnenburg et al., 2006]

Alignment Algorithms


InputTwo sequences over the alphabet {A, C, G, T, N}

EST sequence SE of length mDNA sequence SD of length n

Substitution matrix M : " ) " . R,where " := {A, C, G, T, N,#}

OutputSequence alignment A

Sequence of pairs, i.e. A = (ar, br)r=1,...,R, ar, br ! "R / m + n depends on the alignment

Alignment that maximizes the alignment score

s(A) =R!

r=1

M(ar, br)

Maximizing the Alignment Score


Needleman-Wunsch algorithmMaximizes alignment score by dynamic programmingFills m · n alignment matrix V :

V (i, 0) := 0 and V (0, j) := 0 for all i, jRecursion

V (i, j) = max

#$

%

V (i # 1, j # 1) + M(SE(i), SD(j))V (i # 1, j) + M(SE(i),& #&)V (i, j # 1) + M(&#&, SD(j))

Runtime time and space complexity: O(m · n)

Problems:Does not distinguish between gaps and intronHow to choose M? No splice site model!Too expensive for alignments against whole genomes

Needleman-Wunsch algorithm


Needleman-Wunsch with Introns


Recursion with Intron Model


Extended recursion formula (0i = 1 . . . m, j = 1 . . . n)

V (i, j) = max

#&&$

&&%

V (i # 1, j # 1) + M(SE(i), SD(j))V (i # 1, j) + M(SE(i),& #&)V (i, j # 1) + M(&#&, SD(j))

max1/k/j#1(V (i, k) + fI(k, j))

For intron score fI(k, j) considerSplice sites scores sDon

k and sAcck (SVM predictions)

- Contribute fDon(sDonk ) + fAcc(sAcc

k )

Length of intron- Contributes fLen(j # k)

Unspecified functions fDon, fAcc, fLen as well as M !

Idea: Learn functions on training set with known alignments

Parameterization


Substitution matrix M : " ) " . RFunctions fLen, fAcc and fDon

Piecewise linear functions (support points x1, . . . , xs):

f (x) =

#&$

&%

"1 x / x1"i(xi+1#x)+"i+1(x#xi)

xi+1#xixi / x / xi+1

"s x $ xs

.

" := ("1, . . . , "s) parametrizes functionLet " := ("Acc, "Don, "Len, "M)

Given ", alignment score s"(A) is fully defined

Parameters: Optimization


IdeaFind " such that for a known alignment A+

s"(A+) 1 s"(A#)

where A# %= A+ is any wrong alignmentGiven N known alignments A+

i , i = 1, . . . , N

Solve quadratic optimization problem (QP)

min!$0,"

1

N

N!

i=1

!i + P(")

s.t. s"(A+i ) # s"(A#

i ) $ 1 # !i 0A#i %= A+

i , i = 1, . . . , N

!i: Slack-variables to implement a soft-marginP("): Regularizer leading to smooth functions

Problem: Exponentially many constraints

Iterative Algorithm


Set " := ("Acc, "Don, "Len, "M) randomly, A#i = *

For t = 1, . . . , T

For i = 1, . . . , N

Compute (wrong) alignments A# based on "If A# %= A+

i , then A#i := A#

i , {A#}Obtain new parameters " by solving the restricted QP

min!$0,"

1

N

N!

i=1

!i + P(")

s.t. s"(A+i ) # s"(A#) $ 1 # !i 0A# ! A#

i , i = 1, . . . , N

Only need to solve small optimization problems!Guaranteed convergence!

Microexon Simulation Study


Artificial DataConsider EST confirmed exon triples (C. elegans)Shorten middle exon in central region (EST & DNA)

(found by blat andstrict filtering)

Microexon generated- Splice sites still intactGenerate insertions/deletions/mutations in artificial EST

(# = 0%, 1%, 2%, 10%, 20%, 50%)Train PALMA on 4608 exon triples (2 1h)Test blat, sim4, exalin and PALMA on 4358 tripplesCorrect only if all boundaries are correctly predicted

Microexon Simulation Study


Artificial DataConsider EST confirmed exon triples (C. elegans)Shorten middle exon in central region (EST & DNA)

(found by blat withstrict post-processing)

- Microexon generated- Splice sites still intactGenerate insertions/deletions/mutations in artificial EST

(# = 0%, 1%, 2%, 10%, 20%, 50%)Train PALMA on 4608 exon triples (2 1h)Test blat, sim4, exalin and PALMA on 4358 tripplesCorrect only if all boundaries are correctly predicted

Results (C. elegans)


Error rate increasesdrastically for blatand sim4

Exalin performsquite well, butalways > 3% wrongPALMA is alwayscorrect for # / 10%

PALMA w/o SS onlyslightly worse

Conclusion


New alignment algorithm for perfect alignments ofmRNA and DNAExploits very accurate SVM-based splice site predictionsNew idea of combining different sources of information:

Similarity, splice site scores and intron lengthsLarge margin based iterative algorithmGuaranteed convergence

Significantly reduced error rates on test data (short ex-ons/much noise)Better detection of microexons & altern. spliced exonsCurrent work: Reduce computational complexitySource code (Python/C++, GPL) and data available at

Substitution Matrix


M : " ) " . Rmatches score high, gaps score lowmismatch scores all close to zero

Donor/Acceptor Score


fAcc and fDon

Score the acceptor and donor SVM outputs

Intron Length Score


fLen

Maximum near 50nt (most frequent intron length)

Discriminative Gene Finding


mGene Talk (30 min)

Computational Approaches to the Analysis of

Whole Genome Resequencing Data

Gunnar Ratsch

Friedrich Miescher Laboratory, Tubingen

Gunnar Ratsch (FML, Tubingen) Computational Approaches for Genome Resequencing 1 / 20

Introduction

What is the genetic basis of variation?

Modified from Koornneef et al. 2004. Ann. Rev. Plant Biology, 55, 141-172.


Introduction

Questions:

What sequence changes occur in short time frames?

Which polymorphisms and genes underlie adaption?

What are the consequences for gene function?

Arabidopsis thaliana:

119 Mb finished euchromatic sequence (Col-0)

Resources comparable to Drosophila and C. elegans

Collections of >1000 wild strains from 3 continents

Strains are largely homozygous

Resequencing of 20 wild strains

genome-wide identification of sequence polymorphisms

High-density oligo-nucleotide arrays for high-throughputresequencing


Resequencing Array Basics I


Resequencing Array Basics II

>99.99% of bases represented

Each base queried with forward and reverse strand probe quartets

Nearly 1 billion oligos per ecotype

19+1 ecotypes surveyed representing worldwide distribution


Resequencing Data

Data analysis challenge

Hybridizationintensities depend on

OligomerEcotypeRepeats

Measurement noise

Identify SNPs

Problematic cases

Highly polymorphicregions

Deletions/insertions


A Brief Excursion to Machine Learning I

Large Margin Learning

Extract features

Find linearseparation

With large margin

Classify new points

Works with

many featuresnonlinearitiesusing kernels

Elegant theory

“Support VectorMachines”


Application to SNP discovery

Classification using Support Vector Machines with 302 features

≈2,400 known SNPs/ecotype (Nordborg et al., PLoS Biol., 2005)

Out-of-sample evaluation and prediction on whole genome

Comparison with Perlegens model based method (Hinds et al., Science, 2005)

Clark et al., in prep., 2006.Gunnar Ratsch (FML, Tubingen) Computational Approaches for Genome Resequencing 8 / 20

Identification of Highly Polymorphic Regions

Results

Performance drops,when other SNPs arein vicinity (1-20nt)

Least predicted SNPsin highly polymorphicregions!

ML more sensitive

New Approach

Polymorphic RegionPrediction (PRP)

Novel ML techniquesfor predicting complexproperties


Modeling polymorphic regions

Example sequence from Bor-4

Create segmentation into

conserved and

polymorphic regions (distance <25nt)

Predict segmentation using state-modelbased approach

conserved

polymorphic


Example

Bor-4, chromosome 5, 14303502...14304007

Known labels

SNPs detected with SNP calling methods

Targetsegmentation

SNP calls

Count prediction as correct if it 75% overlaps

55% Sensitivity, 90% Specificity (excluding isolated SNPs)

Previously: Heuristic method with much lower sensitivity


Example

Bor-4, chromosome 5, 14303502...14304007

50 100 150 200 250 300 350 400 450 500 550

0123

Input feature: hybridization intensities

Known labels

Targetsegmentation

SNP calls





Example

Bor-4, chromosome 5, 14303502...14304007

50 100 150 200 250 300 350 400 450 500 550

0123

Known labels

Prediction of a polymorphic region (PRP)

Targetsegmentation

SNP calls





Complementing SNP Calls

1 [2,3] [4,5] [6,10] [11,20] [21,50] [51,100] >100 0

0.2

0.4

0.6

0.8

1

SNPs covered by PRPs, TP rate SNP calls, TP rate

Distance from SNP to nearest polymorphism

SN

P d

etec

tion

true

pos

itive

rat

e

Fraction of called/covered polymorphisms (test set):

SNP calling (MB+ML) Region predictorSNPs ∼32% ∼41%SNPs both methods ∼65%Deletions (per base) ∼71%Insertions ∼39%


Polymorphism Distribution

28.0

15.9

4.9

8.5

14.2

3.6

6.0

35.4

3.1

4.7

43.2

5.3

5.1

14.8

35.5

3.3

55.6

13.3

Coding 230,186 3,828,824

Intron 96,069 4,090,306

Untranslated RNA 32,771 1,029,948

Intergenic 229,335 16,046,419

Pseudogene 21,552 1,413,369

Transposon 38,657 2,462,213

SNP no. bp in PSPsSequence type

Inner circle: genomic basesInner ring: SNP predictionsOuter ring: bases in PRPs

Coding regions are underrepresented for PRPs while transposons areoverrepresented.

Clark et al., Zeller et al., in preparation, 2006Gunnar Ratsch (FML, Tubingen) Computational Approaches for Genome Resequencing 13 / 20

Predicted Effects on Gene Products

SNPs may interfere with signal recognition

Transcription start & stop

Splice sites

Translation start & stop

Regulatory elements

Consequences

Modification of consensus sequence (e.g. splice site dinucl.)

Permanent change⇒ Easy to check

Weaker or stronger recognition of signals

Different expression levels(Alternative) splicing pattern may change

⇒ Needs ab initio gene finding ⇒ build on our previous work


Effects on Genes

SNPs (MB+ML) leading to consensus changes

109,976 amino acid changes

1,227 premature stops

156 initiation methionine changes

435 splice site changes

Major changes in 573 genes validated by dideoxy sequencing∗

Polymorphic Regions Predictions

Overlap coding regions of 16,692 genes in at least one ecotype

50% overlap in 1,910 genes, 95% overlap in 743 genes

122 coding sequence deletions validated by dideoxy sequencing∗

∗ Verified in collaboration with laboratory of Joseph Ecker


Major Effects Distribution


Predicted Effects by Gene Finding (Preliminary)


Example of Predicted Splice Form Change

bur 0 +145 106 200 64 351383 90 397 85

bor 4 +145 79 106 200 64 351196 108 90 397 85

br 0 +145 106 200 64 351383 90 397 85

c24 +145 106 200 64 351383 90 397 85

cvi 0 +145 106 200 64 351383 90 397 85

got 7 +145 106 200 64 351383 90 397 85

ler 1 +145 79 106 200 64 351

196 108 90 397 85

lov 5 +145 106 200 64 351

383 90 397 85

nfa 8 +145 106 200 64 351

383 90 397 85

tsu 1 +145 79 106 200 64 351

196 108 90 397 85

bay 0 +145 79 106 200 64 351

196 108 90 397 85

est 1 +145 106 200 64 351

383 90 397 85

fei 0 +145 106 200 64 351

383 90 397 85

rrs 10 +145 106 200 64 351

383 90 397 85

rrs 7 +145 106 200 64 351

383 90 397 85

sha +145 106 200 64 351

383 90 397 85

tamm 2 +145 106 200 64 351

383 90 397 85

ts 1 +145 106 200 64 351

383 90 397 85

van 0 +145 106 200 64 351

383 90 397 85

Col 0 +145 106 200 64 351

383 90 397 85

annotation +145 106 200 64 351

383 90 397 85

1 2 3 4 5 6

768 1152 1536 1920 2304

AT4G02980Chromosome 4 +


Conclusions

Created inventory for polymorphisms in Arabidopsis thaliana

Highly polymorphic: ≈0.5% in SNPs, ≈25% in PRPs

New method for SNP calling; more accurate than Perlegen’s

Accurate polymorphic region predictions

Important for further analysis (e.g. dideoxy sequencing)

Large number of major effect changes

Overrepresented in R genes, F-box genes, Receptor-like kinases

More predicted changes by ab initio gene finding

Application to other genomes (rice, human?)

Study variations using mRNA tiling arrays

Expression levels, splicing, . . .


Acknowledgments

Friedrich Miescher Laboratory

Gabriele Schweikert

Georg Zeller

The Salk Institute, CA

Paul Shinn

Joseph Ecker

MPI for Biological Cybernetics

Bernhard Scholkopf

MPI for Developmental Biology

Richard Clark

Stephan Ossowski

Norman Warthmann

Detlef Weigel

ZBIT, University of Tubingen

Daniel Huson

Perlegen Sciences, CA

Kelly Frazer


Summary Of Lectures

Cheng Soon Ong, Petra Philips and Gunnar Rätsch: Kernel Methods for Predictive Sequence Analysis: Introduction, Page 33

Statistical Learning TheoryProbabilistic ApproachesSupport Vector MachinesConvex OptimizationBoostingIntroduction to (String) KernelsFast SVMs using String KernelsGraph kernelsMultiple Kernel LearningStructured Output LearningApplications

Probabilistic Learning Model

G. Rätsch, C.S. Ong and P. Philips: Advanced Methods for Sequence Analysis, Page 17

AssumptionAll data is generated by the same hidden probabilisticsource!

Formally! is an unknown joint probability distribution over X!Y

Training data ((x1, y1), . . . , (xn, yn)) is iid " !

Aim: find best f # $ F that minimizes risk

R(f ) =

!"(f (x), y)d!.

ERM: find best fn $ F that minimizes empirical risk

Remp(f ) =1

n

n"

i=1

"(f (xi), yi).

Generative vs Discriminative


Generative approachModels p(x, y) = p(x|y)p(y). Uses Bayes’ rule to infer

p(y|x) =p(x|y)p(y)

p(x).

Discriminative approachModels p(y|x) directly and takes max.

ExamplesGenerative: Mixtures of Gaussians, Hidden MarkovModels, Bayesian Networks, Graphical Models, · · ·Discriminative SVM, (Regularized) Least SquaresRegression, · · ·

SVMs: Geometric View

Cheng Soon Ong and Gunnar Rätsch: Kernel Methods for Predictive Sequence Analysis: Introduction, Page 2

Minimize

1

2!w!2 + C

N"

i=1

!i

Subject to

yi("w,xi# + b) ! 1 $ !i

!i ! 0for all i = 1, . . . , N.

The examples on the margin are called support vectors[Vapnik, 1995]Called the soft margin SVM or the C-SVM [Cortes andVapnik, 1995]

Convex Optimization


Constrained Optimization (generally hard)minx f0(x)

subject to fi(x) " 0 for all igj(x) = 0 for all j

Convex Optimization (generally easy)minx f0(x)

subject to fi(x) " 0 for all ia%j x = bj for all j

f0, f1, . . . , fm are convex, and the equality constraints areaf!ne Boyd and Vandenberghe [2004].

Nonlinear Algorithms in Feature Space


Linear separation might be not sufficient!& Map into a higher dimensional feature space

Example: all second order monomials

! : R2 ' R3

(x1, x2) (' (z1, z2, z3) := (x21,)

2 x1x2, x22)

!

!

!

!

!

!

!

!

"

"

"

"

"

"

"

"

"

"

""

"

"

"

"

"

"

"

"

x1

x2

!!

!!

!

!

!

!

"

"

"

"

"

"

"

"

"

"

"

"

"

z1

z3

"

z2

AdaBoost (Freund & Schapire 1996)

Machine Learning Summer School, July 2006 in Taipei. Gunnar Rätsch: An Introduction to Boosting. Part I (The Idea of Boosting), Page 15

Idea:Simple hypotheses are not perfect!Hypotheses combination ! increased accuracy

Problems:How to generate different hypotheses?How to combine them?

Method:Compute distribution d1, . . . , dN on examplesFind hypothesis on the weighted training sample(x1, y1, d1), . . . , (xN, yN, dN)

Combine hypotheses h1, h2, . . . linearly:

f =T!

t=1

!tht

Example: Trees & Tries


Tree (trie) data struc-ture stores sparseweightings on se-quences (and theirsubsequences).

Illustration: Threesequences AAA, AGA,GAA were added to atrie (!’s are the weightsof the sequences).

Building tree: O(Q · L · D)

Compute all f (xi): O(N ·L ·D)

Memory: O(Q · L · D · |!|)Works for any D

44

Definition of Diffusion Kernel

• A: Adjacency matrix, • D: Diagonal matrix of Degrees• L = D-A: Graph Laplacian Matrix• Diffusion kernel matrix

– Diffusion paramater

• Matrix exponential, not elementwise exponential

Summary


MKL Algorithm

Automatically computes best convex combinationof kernels

k(x,x!) =M!

p=1

"pkp(x,x!),M!

p=1

"p = 1, "p " 0

SILP formulation makes large scale training andevaluation possible.

Possible Applications

Heterogeneous data.Improving interpretability.

Max-Margin Structured Output Learning


Learn function f (y|x) scoring segmentations y for x

Maximize f (y|x) w.r.t. y for prediction:

argmaxy#Y$

f (y|x)

Given N sequence pairs (x1,y1), . . . , (xN,yN) for trainingDetermine f such that there is a large margin betweentrue and wrong segmentations

minf

CN!

n=1

#n + P[f ]

w.r.t. f (yn|xn) % f (y|xn) " 1 % #n

for all yn &= y # Y$, n = 1, . . . , N

Exponentially many constraints!

Modeling polymorphic regions

Example sequence from Bor-4

Create segmentation into

conserved and

polymorphic regions (distance <25nt)

Predict segmentation using state-modelbased approach

conserved

polymorphic


SVM S3VM Training a S3VM SSL Assumptions + Methods Summary

Called Label Propagation, as the same solution is achieved byiteratively propagating labels along edges until convergence

[images from “Learning with Local and Global Consistency”, Zhou, Bousquet, Lal, Weston, Scholkopf; NIPS 2004]

Note: herecolor

!= classes

Ulrik

evo

nLuxb

urg

:PCA

and

Ker

nel

PCA

6.

Dec

ember

2006

27

Summary PCAKeep in mind the following picture:

A Brief Excursion to Machine Learning II

Problems with Mature Solutions

Machine Learning works well for relatively sim-ple objects with simple properties:

Classification

Regression

(Novelty detection)

Current Research

Large scale problems (>10 million examples)

Classification of structured objects, e.g. sequences, networks etc.

Improving interpretability of learning results

Prediction of complex properties

Sonnenburg et al., Journal of Machine Learning Research, 2006:http://www.fml.mpg.de/raetsch/projects/shogun.


References

L. Florea, G. Hartzell, Z. Zhang, G.M. Rubin, and W. Miller. A computer program for aligning a cdna sequence with a genomic dnasequence. Genome Research, 8:967–974, 1998.

W. J. Kent. BLAT–the BLAST-like alignment tool. Genome Res, 12(4):656–664, April 2002.

R. Mott. EST GENOME: a program to align spliced dna sequences to unspliced genomic dna. Comput. Appl. Biosci., 13:477478, 1997.

G. Ratsch and S. Sonnenburg. Accurate splice site detection for Caenorhabditis elegans. In K. Tsuda B. Schoelkopf and J.-P. Vert, editors,Kernel Methods in Computational Biology. MIT Press, 2004.

Soren Sonnenburg, Gunnar Ratsch, Christin Schafer, and Bernhard Scholkopf. Large Scale Multiple Kernel Learning. Journal of MachineLearning Research, 7:1531–1565, July 2006.

S.J. Wheelan, D.M. Church, and J.M. Ostell. Spidey: a tool for mrna-to-genomic alignments. Genome Research, 11(11):1952–7, 2001.

M. Zhang and W. Gish. Improved spliced alignment from an information theoretic approach. Bioinformatics, 22(1):13–20, January 2006.

advanced methods for sequence analysis · sim4 [florea et al., 1998], spidey [wheelan et al., 2001]...

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